How to remove parent category path from sub category url in Magento

Go to app/code/core/Mage/Catalog/Model/

Open Url.php and go to line no 632 and comment(//) the below line

//if (null === $parentPath) {
//$parentPath = $this->getResource()->getCategoryParentPath($category);
//elseif ($parentPath == '/') {
$parentPath = ''; //('Don't comment it')

Now save and upload it.

Now login to admin panel of your site then go to System->Config->Index Management and click on select all then select Reindex Data from the Action Dropdown then click on submit.

Now refresh your cache to see the effect.